The high-order completeness analysis of the scaled boundary finite element method

The scaled boundary finite element method (SBFEM) is a novel semi-analytical approach. The high-order completeness analysis is an important and necessary part of the basic theory of the SBFEM. Different from the standard FEM, the shape functions are constructed by the computation of the SBFEM. Thus,...

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Published inComputer methods in applied mechanics and engineering Vol. 362; p. 112867
Main Authors Jia, Yan-Mei, Li, Chong-Jun, Zhang, Ying, Chen, Juan
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.04.2020
Elsevier BV
Subjects
Bubble functions
Completeness
Finite element
Finite element analysis
Finite element method
High-order completeness
Higher order accuracy
Mathematical analysis
Patch tests
Polynomials
Scaled boundary finite element
Semi-analytical
Shape functions
Scaled boundary finite element
Bubble functions
Semi-analytical
High-order completeness
Higher order accuracy
Finite element
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Summary:The scaled boundary finite element method (SBFEM) is a novel semi-analytical approach. The high-order completeness analysis is an important and necessary part of the basic theory of the SBFEM. Different from the standard FEM, the shape functions are constructed by the computation of the SBFEM. Thus, the key is to show that the polynomials bases can be always obtained independently of the shape of the S-elements. This paper presents the theoretical analysis of the high-order completeness of the SBFEM in mathematics for two- and three-dimensional problems, including the curved boundary elements. Moreover, in the completeness analysis, we also make up some theoretical problems and give the necessary proofs in the solving procedure of the SBFEM. Some numerical patch tests verify the theoretical results.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2020.112867